I don't really have any experience with lizards and I can't recommend the two common beginning turtles, sliders and box turtles, because both need lots of room and neither is as easy to care for as most people think. Mud and musk turtles are small and sedentary and make pretty good pets but you'd have to use some other kind of enclosure; a twenty-gallon aquarium would be fine.
If you're willing to bend on the no-mice rule, corn snakes are really great pets. They get larger than previously stated; mine is a little over five feet, but he's very docile and inquisitive and loves to come out. And unless snake's cage will frequently get below the 60s, you don't need any heating equipment.